Question

The value of "x" for which the point (x,-1) (2,1) & (4,5) are collinear will be. a)0 b)1 c)2 d)3



Answer
b)1​

Answer 1

Given :-

Points (x, -1) , (2,1) & (4,5)

To Find :-

Value of x

Solution :-

Let

A(x, -1) , B(2,1) & C(4,5)

Since they are collinear

${\large{\boxed{\underline{\bf{Slope\;of\;AB=Slope\;of\;BC}}}}}$

$\rm :\implies \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_2-y_1}{x_2-x_1}$

$\rm :\implies \dfrac{1-(-1)}{2-x}=\dfrac{5-1}{4-2}$

$\rm :\implies \dfrac{1+1}{2-x}=\dfrac{4}{2}$

$\rm :\implies \dfrac{2}{2-x}=2$

$\rm :\implies 2=2(2-x)$

$\rm :\implies 2=4-2x$

$\rm :\implies 2x=4-2$

$\rm :\implies 2x=2$

$\rm :\implies x=\dfrac{2}{2}$

$\rm :\implies x=1$

Therefore,

Value of x is 1